Simplicity of augmentations of codimension 1 germs and by Morse functions

I. Breva Ribes; R. Oset Sinha

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arXiv · 2203.09223

Simplicity of augmentations of codimension 1 germs and by Morse functions

I. Breva Ribes·R. Oset Sinha

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Abstract

We study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the augmentation comes from an $\mathscr{A}_e$-codimension 1 germ or the augmenting function is a Morse function, we give a complete characterisation for simplicity. These characterisations yield all the simple augmentations in all explicitly obtained classifications of $\mathscr{A}$-simple monogerms except for one ($F_4$ in Mond's list from $\mathbb{C}^2$ to $\mathbb{C}^3$). Moreover, using our results we produce a list of simple augmentations from $\mathbb{C}^4$ to $\mathbb{C}^4$.

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I. Breva Ribes, R. Oset Sinha. 2022-03-17. Simplicity of augmentations of codimension 1 germs and by Morse functions. https://arxiv.org/abs/2203.09223

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